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From: "Abel Brown" <brown.2179@osu.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Voronoi diagram on a sphere
Date: Fri, 6 Nov 2009 22:42:03 +0000 (UTC)
Organization: The Ohio State University
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> Hi Abel,
> 
> You should realize this is an approximate Voronoi diagram.
> The fewer points you have the less accurate it will be.
> Also, the Voronoi vertices are not exactly on the surface of the sphere, as 
> the triangle facet is not "draped" over the surface, but it's not difficult 
> to project them.
> 
> If you wish to compute the Voronoi region associated with point  "i " you 
> can do so as follows;
> 
> 1) Compute the set of triangles attached to point i. The triangles are 
> arranged in a CCW cycle around the point i.
>      Ti = tr.vertexAttachments(i)
> 
> 2) The positions of the vertices defining the i'th Voronoi region are the 
> circumcenters of these triangles
>      ccTi = tr.circumcenters(Ti)
> 
> 3) The Voronoi region may be non-planar.
>      To compute the area break it into triangles defined by the point i and 
> each edge of the Voronoi region.
>      The location of point i is x(i), y(i), z(i)
>       the two edge points are ccTi(1,:) to ccTi(2,:)
> 
> I suggest you first try computing a simple 2D Voronoi diagram using this 
> approach, and when you understand the process apply it to your problem.
> Take your time, understand the steps, and if you get stuck feel free to 
> contact me directly.
> 
> 
> Damian
> 

Damian

This works great! 

No problems computing polygon for each point using your instructions!

Thanks again
-abel